Analog four quadrant divide circuit



,xpr'ilzz., 1970'4 M NEWMAN ETAL 3,509,332

ANALOG FOUR QUADRANT DIVIDE CIRCUIT Filed June 3. 1968 2 Sheets-Shet l April 23, 1970 B. J. NEWMAN Em. 3,509,332

ANALOG FOUR QUADANT DIVIDE CIRCUIT INVENTORS BY y/A W. @.g

any.;

United States Patent Oce 3,509,332 Patented Apr. 28, 1970 U.S. Cl. 23S- 196 4 Claims ABSTRACT OF THE DISCLOSURE An analog four quadrant dividing device is described comprising servo means and a follow-up potentiometer, a high gain first operational amplifier connected to receive a first analog voltage input (Binh and a feedback voltage from a potentiometer which is positioned with the followup potentiometer so as to provide an output Eb, a diode function generator connected to receive a second analog voltage input (Em)2 and characterized by a transfer function such that it provides an output Ea to the servo means which is equal in magnitude to (E1n)2 when |(E1n)2l a predetermined value Z, and is equal to Z when |(Ein)2[ Z, whereby useful values of Eb may be obtained irrespective of one or the other of the inputs approaching zero, the device further comprising voltage comparator, relay, and additional operational ampli-fier means operative to produce from Eb a final output E, of proper sign.

STATEMENT OF GOVERNMENT INTEREST The invention described herein may be manufactured and used by or for the Government of the United States of America for governmental purposes without the payment of any royalties thereon or therefor.

BACKGROUND OF THE INVENTION This invention relates to devices for effecting mathematical computations and more particularly to an irnprovedV analog, four quadrant dividing device of the type utilizing relay or other switching means for effecting a change of sign when one or the other of the usual two inputs changes sign, thereby always providing a quotient of the proper sign. Such devices have utilized potentiometer means positioned by servomotor means driven by servoamplifier means in response to one of the analog voltage inputs and operational amplifier means responsive to the other input and a potentiometer value to provide an output voltage representative of the quotient.

One of the salient weaknesses or limitations of such practice has been the fact that as the denominator input approaches zero, the operational amplifier becomes overloaded and results in gross inaccuracies. Thus, that type of circuit cannot effectively be used with small denominator values.

SUMMARY OF THE INVENTION With the foregoing in mind, it is primary object of this invention to provide an improved analog, dividing device which can be effectively utilized with small denominator values.

It is another object of the invention to provide a four quadrant analog dividing device which can be utilized with small denominator values and provides outputs of the proper sign irrespective of shifting of the signs of the inputs.

As another object this invention aims to accomplish the foregoing through the provision of a dividing device comprising multiplier servo means for positioning potentiometer means, operational amplifier means for combining one of the device inputs with potentiometer values, and

diode function generator means for providing a voltage to the multiplier servo means, the value of which voltage is a predetermined function of another of the inputs to the device. In one preferred embodiment of the invention there is further included a comparator means and relay means for assuring that the output of the device has a sign which is consistent with the signs and values of the lnputs.

BRIEF DESCRIPTION OF THE DRAWING The invention may be further said to reside in certain constructions and arrangements of parts as will be better understood from the following description of a preferred embodiment when read in conjunction with the accompanying sheets of drawings forming a part of this specification, and in which:

FIG. 1 is a diagrammatic illustration of an analog four quadrant dividing device embodying the present invention; and

FIG. 2 is a graphic illustration of the output of the diode function generator portion of the device of FIG. l.

DESCRIPTION OF THE PREFERRED EMBODIMENT In the form of the invention illustrated in FIG. 1 and described hereinafter, there is provided an analog, four quadrant dividing device, generally indicated at 10. The device 10 comprises first and second input connections 12 and 14 to which are applied voltages (Binh and (Binh which are analog representations of a variable dividend Y and a variable divisor X, respectively.

The input connection 14 is connected as shown by line 16 to apply the voltage (Em)2 to a diode function generator 18, and by line 20 to a voltage comparator 22. The diode function generator 18 provides on line 24 an output voltage Ea, the value of which is a predetermined function of the value of the input voltage (Binh. Referring to FIG. 2, the values of output Ea of the diode function generator 18 for different values of input (Em)2 are represented by the curve 28.

It will be seen from FIG. 2 that for positive or negative inputs (Em)2 which are of one volt or greater in magnitude, the output E, of the diode function generator 1-8 is a positive voltage of the same magnitude as the input. For inputs (Em)2 of magnitude less than one volt, either positive or negative, the output E8L is one volt, positive. The diode function generator 18 may be of any construction which will provide an output which corresponds in magnitude to the input whenever the input is greater than a predetermined finite value Z, and an output which is at the predetermined value for any input which is lesser in magnitude than that value. In the present example the value Z is one volt, positive. The construction of such function generators is well known to those skilled in the art to which the invention pertains and the details thereof are not necessary to an understanding of the invention. Suffice it to say that the diode function generator may be any one of a number of commercially available units such as the Donner Model 3S sold by Donner Scientific Company of Berkeley, Calif., or such as are found in the analog computer units sold by Reeves Instrument Corporation of New York City, all of which are constructed according to the principles set forth in the work entitled Methods for Solving Engineering Problems Using Analog Computers, published by McGraw-Hill, 1964. All of these diode function generators are provided with simple potentiometer controls for selecting the slopes of segments of the function, for selecting the breakpoints between segments, and for inserting constant values such as the value referred to as Z, above.

The output signal 'Ea of the diode function generator 18 is applied as shown by line 24 to a multiplier servo 30 which conveniently comprises a conventional electromechanical folloW-up device. The servo 30 is mechanically linked, as indicated at 32, to the movable element or wiper of a potentiometer 36 -which is ganged with the movable element or wiper of a second potentiometer 40, the mechanical connection therebetween being indicated by the dotted line 42. The potentiometer 36 has its resistance portion connected 'between ground and a source of potential which is 100 volts positive in this embodiment.

The output of the potentiometer 36 is fed back via line 44 to the input of the servo 30 so that the potentiometers 36 and 40 are moved to assume positions proportional to the output Ea of the diode function generator 18. Because of the previously described transfer function of the diode function generator, it will be noted that the potentiometer 40 will thus be positioned in accordance with the magnitude of the input (Em)2, irrespective of the sign thereof when |(Ein)2|l, and proportional to an input of l when |(En)2| l. In this example the proportionality will involve a factor K of 100 (established by the potential across potentiometer 36) so that the servo shaft and potentiometer Wiper positions are representative of Ea/ 100;

The potentiometer 40` forms part of a feedback circuit for an operational amplifier 48 which receives as its primary input the Y variable analog voltage (Em)2 via line 46. Thus, the potentiometer 40 is connected between the output line 50 of amplifier 48 and ground, and the Wiper thereof is connected as shown by line 52 to apply a voltage Ef derived from the potentiometer 40 as a feedback input to that operational amplifier.

The operational amplifier 48 is connected in a high gain configuration and, according to operational amplifier theory, the summation of the voltage inputs thereto must equal zero. Thus:

(Ein)1i (Ef) :0 (l) Now, the output Ef of the Wiper of the potentiometer 40 is the product of the output Eb of the operational amplifier 48 on lines 50, 54, and the position of the potentiometer wipers. That is to say,

Jl@ E- ico (2) Since (Em)1=Y (2) and Ea=X, when IXII V(4) substitution of Equations 2 and 4 into Equation 1 yields:

Since Ea is never less than 1 because of the transfer function of the diode function generator, and because of the proportioning factor K, Eb will accurately equal iooY for 99% of the range of operation of the device 10, eX- cept perhaps for sign. For those situations Where (Em)2 is less than l or zero, there will be a resulting error, but because Ea will always have a finite value of at least 1,

there will be no overloading of the operational amplifier 48 as would occur if (Em)2 were applied directly to the servo 30 and X equalled or approached zero.

The invention contemplates the inclusion of means to insure that the final output of the device 10, which will be termed Bout, is of the proper sign. Thus, the comparator 22 receives the X input (Em)2 via line 20 and compares it to a reference voltage level E1r which in the embodiment being described is taken to be ground level as indicated by the connection 5'6. The comparator 22 is connected as shown by line 58 to control energization of a relay :60, the output voltage Ec of the comparator on line 58 being characterized by the following relationships:

when (Einh: (Er) 0, then Ec=0 (8) and when (En)2= (EOSO, then Ec=6 volts (9) The relay 60 comprises a contactor 62 which is connected to receive the output Eb of amplifier 4S via line 54. The contactor 62 is movable between contacts 64 and 66, the contactor being in engagement with the former when energized and with the latter when deenergized. Energization of the relay 60 is effected by the -6 volt condition of En.

The contact 64 is connected as shown by line 68 to the input of an operational amplifier 70, while the contact 66 is connected as shown by line 72 to the input of an operational amplifier 74. The amplifier 70 has its output connected via line 7'6 as an input to the amplifier 74. The latter has its output Eout connected by line 78 to an output connection 80.

The amplifiers 70 and 74 are so connected that each has a gain of l. Thus Eout=nEb when the relay '60 is deenergized, and

Eout= (-Eb) or Eb when the relay is energized.

Accordingly, the device 10 will not only provide a useful value of EonG even when X approaches zero, but will also automatically produce Bout with the correct sign or polarity.

From the foregoing detailed description it will be appreciated that the previously stated objects and advantages, as Well as others apparent from this specification, have been achieved by the four quadrant dividing device 10 embodying this invention.

Obviously many modifications and variations of the present invention are possible in the light of the above teachings. It is therefore to -be understood that the invention may be practiced otherwise than as specifically described.

What is claimed is: 1. An analog dividing device comprising: multiplier servo means connected to receive as an input a voltage Ea;

follow-up means responsive to said servo means and connected to provide feedback voltage thereto whereby said servo means seeks a position proportional to the input thereto;

operational amplifier means connected to receive an input (Emh which is an analog representation of a first variable, said operation amplifier being connected in high gain configuration and providing an output signal Eb;

means responsive to Eb and the position of said servo means to provide a feedback input Ef to said operational amplifier such that said device being further characterized by the improvement comprising diode function generator means connected to receive an input (Em)2 which is an analog representation of a second variable, said diode function generator providing as an output said voltage Ea to said servo means, said voltage Ea being characterized by the relationship:

Ea`=[(Em)2| when [(Emhiz where Z is a predetermined finite value, and

Ea=Z i when |EmQ2| Z voltage comparator means responsive to (Em)2 and a reference voltage Er to provide an output Ec having a first predetermined value under the condition (Em)2}-Er0, and having a second predetermined value under the condition (Em)2|-Er 0;

additional operational amplifier means, said additional operational amplifier means being characterized by a gain of -l; and

relay means responsive to Ec to apply Eb to said additional operational amplifier means so as to provide an output Em which has a sign appropriate to the signs of (Emh and (Binh.

2. An analog dividing device as defined in claim 1, and

wherein:

said follow-up means and said means responsive to Eb and the position of said servo means comprise first and second potentiometers, respectively.

3. An analog dividing device as defined in claim 1, and

wherein:

said additional operational amplifier means comprises two operational amplifiers each having a gain of 1;

said relay means having first and second operative positions, one of which routes Eb through only one of said two operational amplifiers to provide Eout, and the other of which routes Eb through both of said two operational amplifiers in series to provide Bout. 4. An analog dividing device as defined in claim 2,

and wherein:

References Cited UNITED STATES PATENTS Giltinan 23S-196 Nathan et al. 23S-197 Patchell et al. 23S-194X Holdo.

Seliger 235-196X Smith 235-194X MALCOLM A. MORRISON, Primary Examiner J. F. RUGGIERO, Assistant Examiner U.S. Cl. X.R. 

